Regions of variability for generalized Janowski functions

Journal Article

2026

Published in: https://www.aimspress.com/article/doi/10.3934/math.2026142?viewType=HTML

Let r is an element of C, s is an element of [-1, 0), 0 <= alpha < 1. Then, Q [r, s, alpha] stands for the set of analytic functions q that is within the open unit disk E, with q (0) = 1, and satisfies the explicit representation q(zeta)=1 + ((1-alpha) r + alpha s)chi (zeta)/ 1+ s chi(zeta) , where chi (0) = 0 and |chi (zeta)|< 1. In this article, we find the regions of variability W-lambda(zeta(0), r, s, alpha) for (z0 )(0)integral q (rho) d rho when q ranges over the class Q(lambda)[r, s, alpha] defined as Q(lambda)[r, s, alpha] = {q E Q [r, s, alpha] : q ' (0) = ((1-alpha) (r-s)) lambda} for any fixed zeta(0) E E and lambda is an element of E-. As a corollary, the region of variability appears for the alternate sets of parameters as well.

• Publication Work Type: Region of variabilityJanowski functionsgeneralized Janowski functionsSchwarz function
• Publisher Name: AIMS